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Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) /
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new direction...
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| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Princeton, NJ :
Princeton University Press,
[2012]
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| Édition: | Course Book. |
| Collection: | Book collections on Project MUSE.
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| Accès en ligne: | Texto completo |
| Résumé: | Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject. |
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| Description: | Description based upon print version of record. |
| Description matérielle: | 1 online resource. |
| Public: | Specialized. |
| ISBN: | 9781400842704 |